Two circles with centres A and A' and having radius = 2 cm

$$\angle$$ BAC = $$120^\circ$$ [since ABA' forms a equilateral triangle] and length of an arc = $$\frac{\theta}{360^\circ}\times2\pi r$$

Perimeter of shaded portion = $$2\times($$ length of arc BC$$)$$

= $$2\times(\frac{120^\circ}{360^\circ}\times2\pi r)$$

= $$2\times(\frac{1}{3}\times2\pi\times2)$$

= $$2\times\frac{4\pi}{3}=\frac{8\pi}{3}$$

=> Ans - (A)